Question

Two tangents making an angle of 60° between them, are drawn to a circle of radius √2cm, then find the length of each tangent.

Answer 1

Length of each tangent is 2.44

Radius of the circle = √2 cm (Given)

Angle of the tangents = 60° (Given)

Let the two tangents of circle be = PA and PB

Centre of the circle = O

Hence,

∠APO = ∠BPO = ∠APB/2

= 60/2

= 30

OA ⊥ AP and OB ⊥ BP.

In ΔOAP,

Tan 30 = OA/PA

1/√3 = √2/PA

PA = √3 ×√2

PA = √6

PA = 2.44

So, PA = PB = 2.44 cm.